On the stationary states in gradient echo imaging

A formalism is presented that concisely describes the magnetization of a sample subjected to a periodic series of RF pulses. In this formalism, the steady state of the magnetization is shown to be a sum of magnetic substates, each with unique contrast characteristics. When more than one substate contributes to a given image, the substates interfere with each other, producing ghosts and other artifacts. Properly designed gradient protocols can image single substates, producing ghost-free images. The contrast of the image depends largely on the choice of the imaged substate. Analytic solutions for unspoiled, RF spoiled, and gradient spoiled magnetizations are presented.